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A Groupoid Approach to Interacting Fermions

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Abstract

We consider the algebra \({{\dot{\Sigma }}}({{\mathcal {L}}})\) generated by the inner-limit derivations over the \({\mathrm{GICAR}}\) algebra of a fermion gas populating an aperiodic Delone set \({{\mathcal {L}}}\). Under standard physical assumptions such as finite interaction range, Galilean invariance of the theories and continuity with respect to the deformations of the aperiodic lattices, we demonstrate that the image of \({{\dot{\Sigma }}}({{\mathcal {L}}})\) through the Fock representation can be completed to a groupoid-solvable pro-\(C^*\)-algebra. Our result is the first step towards unlocking the K-theoretic tools available for separable \(C^*\)-algebras for applications in the context of interacting fermions.

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Authors and Affiliations

  1. Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands

    Bram Mesland

  2. Department of Physics and Department of Mathematical Sciences, Yeshiva University, New York, NY, 10016, USA

    Emil Prodan

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  1. Bram Mesland
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  2. Emil Prodan
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Correspondence to Emil Prodan.

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Communicated by Y. Kawahigashi

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Emil Prodan was supported by the U.S. National Science Foundation through the Grants DMR-1823800 and CMMI-2131760.

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Mesland, B., Prodan, E. A Groupoid Approach to Interacting Fermions. Commun. Math. Phys. 394, 143–213 (2022). https://doi.org/10.1007/s00220-022-04397-8

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